Thursday, January 24, 2013


In response to my last post, Jackie asks:
Not sure I understand your point about selling in as short a time window as possible. The day-to-day fluctuations of a stock's price is greater than its fluctuation over a week or so, right? But it might not be worth the extra transaction costs to sell over a time window.
I am replying here so the response is more widely visible. I claim that a stock should have much greater fluctuation at the end of a week than a day. In order to have less variance after a week, the stock would have to revert towards some sort of mean after the daily fluctuation. If this was true, I could use a simple strategy to make huge amounts of money in a short amount of time. I would look at a rolling average of one day for all stocks on the market. I would then buy the lowest stocks relative to their mean and then sell when their price hits the mean. The reason this strategy won't work is because stocks will not revert to a mean in the short-term. The reason they don't revert to a mean is because other investors in the market (especially high-frequency traders) would pick up on such an obvious pattern and take advantage of it. These traders would have a smoothing effect on stock price, ensuring that the price never reverts from the mean. Therefore I think it is necessary that variance increases the further into the future you consider.


Jackie said...

But the variance of the stock price from now into the future isn't really what you care about. The point of spreading your buys or sells over a period of time is to be close to the mean of that longer period. Since you're sampling multiple points from the period, so you're more likely to be close to the mean of that period than sampling just one point.

Byron Knoll said...

Because the variance keeps increasing over time, the distribution of the mean over the longer period actually has a higher variance than the distribution of sampling a single point immediately. If this wasn't true, the strategy I mentioned in the post could be used to make huge amounts of money.